103 research outputs found
A continuation method for tensor complementarity problems
We introduce a Kojima-Megiddo-Mizuno type continuation method for solving
tensor complementarity problems. We show that there exists a bounded
continuation trajectory when the tensor is strictly semi-positive and any limit
point tracing the trajectory gives a solution of the tensor complementarity
problem. Moreover, when the tensor is strong strictly semi-positive, tracing
the trajectory will converge to the unique solution. Some numerical results are
given to illustrate the effectiveness of the method.Comment: 15 pages, 4 table
Properties of Some Classes of Structured Tensors
In this paper, we extend some classes of structured matrices to higher order
tensors. We discuss their relationships with positive semi-definite tensors and
some other structured tensors. We show that every principal sub-tensor of such
a structured tensor is still a structured tensor in the same class, with a
lower dimension. The potential links of such structured tensors with
optimization, nonlinear equations, nonlinear complementarity problems,
variational inequalities and the nonnegative tensor theory are also discussed.Comment: arXiv admin note: text overlap with arXiv:1405.1288 by other author
Copositivity for a class of fourth order symmetric tensors given by scalar dark matter
In this paper, we mainly discuss the analytic expression of exact
copositivity of 4th order symmetric tensor defined by the special physical
model. We first show that for the general 4th order 2-dimensional symmetric
tensor, it can be transformed into solving the quadratic polynomials, and then
we give a necessary and sufficient condition to test the copositivity of 4th
order 2-dimensional symmetric tensor. Based on this, we consider a special 4th
order 3-dimensional symmetric tensor defined by the vacuum stability for
scalar dark matter, and obtain the necessary and sufficient
condition for its copositivity.Comment: 16 page
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